Pith Number

pith:X2ZOAINY

pith:2018:X2ZOAINYOYOLS4I6IEOVUFUI3E

not attested not anchored not stored refs pending

Random walks and random tug of war in the Heisenberg group

Diego Ricciotti, Juan Manfredi, Marta Lewicka

arxiv:1811.04765 v2 · 2018-11-08 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X2ZOAINYOYOLS4I6IEOVUFUI3E}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-17T23:47:29.593604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

beb2e021b8761cb9711e411d5a1688d90747c699c780a59988b7c10648c826ee

Aliases

arxiv: 1811.04765 · arxiv_version: 1811.04765v2 · doi: 10.48550/arxiv.1811.04765 · pith_short_12: X2ZOAINYOYOL · pith_short_16: X2ZOAINYOYOLS4I6 · pith_short_8: X2ZOAINY

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/X2ZOAINYOYOLS4I6IEOVUFUI3E \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: beb2e021b8761cb9711e411d5a1688d90747c699c780a59988b7c10648c826ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31752a8e142986eaade1da35b975295d5bd60bab24ebb65f4d36ff6936ff0f66",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-11-08T23:46:27Z",
    "title_canon_sha256": "619a5529a3de66467749bba0182847761c3f9a6c1decd058389a14c1f73f834e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.04765",
    "kind": "arxiv",
    "version": 2
  }
}